Question 4
$$
\max\{|x|-1, x^2-1\} \leq \min\{x^2-1, 1-x\},
$$
where $\max\{a,b\} = \begin{cases} a, & \text{if } a \ge b \\ b, & \text{if } a \lt b \end{cases}$, and $\min\{a,b\} = \begin{cases} b, & \text{if } a \ge b \\ a, & \text{if } a \lt b \end{cases}$.
\max\{|x|-1, x^2-1\} \leq \min\{x^2-1, 1-x\},
$$
where $\max\{a,b\} = \begin{cases} a, & \text{if } a \ge b \\ b, & \text{if } a \lt b \end{cases}$, and $\min\{a,b\} = \begin{cases} b, & \text{if } a \ge b \\ a, & \text{if } a \lt b \end{cases}$.